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Ellie Baker

For me, creating visual art reflects a quest for deeper understanding--of science, mathematics, society, or self--and a wish to share the quest.

This piece is an outgrowth of an extended research project with Susan Goldstine on applications of mathematics to bead crochet. Bead crochet’s spiral structure creates constraints that make it especially challenging to produce symmetric designs, but its stretchiness and flexibility give it a topological flavor that lends itself nicely to torus knot explorations. In our forthcoming book, “Crafting Conundrums: Puzzles and Patterns for the Bead Crochet Artist” (AK Peters/CRC Press), we devote a chapter to torus knots, going from thought experiments to practical bead crochet constructions.

The Torus Traveler's Journey

10 x 20 inches

Bead crochet (glass beads and thread), colored pencil on mylar.

2013

Torus knots, while complex and beautiful to behold, are mathematically simple to describe as a line with slope q/p on a flat torus, where p and q are coprime. This piece provides a window into a conceptual infinite graph with p on the vertical axis and q on the horizontal axis. For p between 3 and 7 and q between 2 and 4, wherever the (p,q) pair is coprime, it shows a bead crochet (p,q) torus knot bracelet and a hand-drawn regular (p/q) star polygon. In the remaining spots, where the (p,q) pair is not coprime and thus neither construction is possible, only the compound star figure is shown. The artwork is intended to invite the viewer to ponder connections between torus knots and star polygons (a topic also discussed in our book).